Best Known (93, ∞, s)-Nets in Base 9
(93, ∞, 222)-Net over F9 — Constructive and digital
Digital (93, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 221)-sequence over F9, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
(93, ∞, 245)-Net over F9 — Digital
Digital (93, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 244)-sequence over F9, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 81 and N(F) ≥ 245, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
(93, ∞, 771)-Net in Base 9 — Upper bound on s
There is no (93, m, 772)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (93, 2312, 772)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92312, 772, S9, 3, 2219), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 249958 992420 973266 677709 493037 546552 017416 626482 308559 295050 256476 304046 666876 114496 704502 436783 177698 223840 555434 160273 072300 040366 399425 850551 476956 358053 050447 120882 539133 732219 849419 112027 337047 457891 148644 138223 494236 306639 763010 165113 235877 795713 892398 741730 779697 484191 038728 133044 186560 606764 045596 553614 641605 101388 448675 904382 641159 497412 449422 425726 306660 119854 128028 707140 944362 717215 135569 549389 455525 461081 206946 171613 368119 707942 957816 732848 275536 207141 367922 605801 432478 225746 361229 811508 857208 839460 861456 323721 844679 089303 484015 314748 483135 099851 311492 420041 890237 310664 453276 586927 677434 758757 599641 142501 515680 028060 666854 638117 367814 402984 765533 514868 584351 495890 292053 264363 520357 259570 914217 388501 113734 378404 966962 187426 686680 128624 371882 070356 344132 681131 685874 248027 808657 917883 282100 144610 349914 480830 828995 512484 887872 780655 416797 222802 232952 622138 476070 545648 077208 482567 412613 067413 331627 387224 913340 732402 449998 250616 096938 200486 989580 547815 002896 094894 204043 511185 197895 451642 682367 450912 826404 617571 615258 118171 611604 453201 859278 091432 001377 694065 116988 542681 426509 123606 684164 300235 060685 279965 950648 317212 789333 603686 140823 476745 412319 414154 754299 573667 326664 708481 377700 760962 569205 927326 469422 490824 183189 620476 091839 458423 754790 238147 877364 060065 188134 902177 630906 480072 931397 430888 259759 055885 406088 875144 279927 386657 627996 664686 871412 894467 662817 196017 641934 869655 822311 668950 969783 040229 092634 429207 693097 284733 805623 971767 254930 800123 048802 225799 636523 202894 037104 015748 338750 879590 218663 219563 243836 851825 015202 161546 643111 380393 941081 246059 592848 615799 869069 892804 787488 201385 040514 846226 310288 070635 312860 488631 859033 722619 474032 334993 149099 721980 561346 978883 975503 157247 967062 882724 366898 201002 625601 942817 912821 375542 928824 910507 253546 450244 197677 424376 844636 099522 507842 617958 442977 272787 847739 657408 263016 588997 017584 288929 234471 893378 508752 169112 397802 879725 555606 791679 219185 202924 259119 489450 728755 964481 951251 846945 148046 507673 830662 493469 247805 191804 733747 925075 257170 055184 427361 942053 375036 157803 423863 335802 307400 730038 295885 713859 453214 274289 575735 027613 984070 911479 628251 564777 750483 493078 851051 547867 576855 545732 066419 734074 634745 923631 462695 004681 / 185 > 92312 [i]
- extracting embedded OOA [i] would yield OOA(92312, 772, S9, 3, 2219), but